The classical Pólya-Szegö principle [1]} states that, given a non-negative function \(f:\mathbb {R}^n\rightarrow \mathbb {R}\) , the Dirichlet integral
\(\int _{\mathbb {R}^n}|\nabla f|^p\)  decreases under suitable rearrangements, the two most common of which are the symmetric decreasing rearrangement about a point and Steiner symmetrization about a hyperplane. Their corresponding Pólya-Szegö inequalities are a powerful tool to approach a wide number of variational problems of geometric and functional nature (see, e.g.,[2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}).
